   Chapter 7.2, Problem 24E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Find the length of the radius of the inscribed circle for a right triangle whose legs measure 6 and 8.

To determine

To find:

The length of the radius inscribed circle for a right triangle whose legs mesure 6 and 8.

Explanation

Formula used:

radius of incircle = Area of incircleperimeter of incircleArea of incircle (A)=s(sa)(sb)(sc)perimeter of incircle (s)=a+b+c2

Given:

The length of the radius inscribed circle for a right triangle whose legs mesure 6 and 8.

Calculation:

Consider the measures of legs of a right triangle 6 and 8.

From the right triangle,

AC2=AB2+BC2

substitute AB=8,BC=6.

AC2=(8)2+(6)2=64+36=100

Taking square root on both sides,

AC=100AC=10

AC=Hypotenuse of the right angle

So we take c=10

Next we find perimeter of triangle,

Let a=8, b=6, and c=10

s=8+6+102s=242s=12

Then we find area of triangle,

Area of<

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